Related papers: On a new incomplete Ricci-flat metric
We construct Ricci flat Kahler metrics with cone singularities along a complex hypersurface. This construction is inspired in part by R. Mazzeo's program in the case of negative Einstein constant, and uses the linear theory developed…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
We express the vacuum Einstein constraints in terms of differential forms - the forms include one-forms constituting an orthonormal coframe of the spatial metric. We show that if the metric is real-analytic, then the constraints can be…
Consider a smooth manifold $M$. Let $G$ be a compact Lie group which acts on $M$ with cohomogeneity one. Let $Q$ be a singular orbit for this action. We study the gradient Ricci soliton equation $\Hess(u)+\Ric(g)+\frac{\epsilon}{2}g=0$…
Starting from the classical notion of an oriented congruence (i.e. a foliation by oriented curves) in $R^3$, we abstract the notion of an oriented congruence structure. This is a 3-dimensional CR manifold $(M,H, J)$ with a preferred…
In the first part of the present paper, we show that O(d,d)-invariance usually known in a homogeneous cosmological background written in terms of proper time can be extended to backgrounds depending on one or several coordinates (which may…
Let $M=G/K$ be a compact homogeneous space and assume that $G$ and $K$ have many simple factors. We show that the topological condition of having maximal third Betti number, in the sense that $b_3(M)=s-1$ if $G$ has $s$ simple factors, so…
We present several new space-periodic solutions of the static vacuum Einstein equations in higher dimensions, both with and without black holes, having Kasner asymptotics. These latter solutions are referred to as gravitational solitons.…
It was previously proved that the G\"{o}del-type metrics with flat three-dimensional background metric solve exactly the field equations of the Einstein-Aether theory in four dimensions. We generalize this result by showing that the…
Along the Ricci flow, we study the polyhomogeneity of complete Riemannian metrics endowed with "a Lie structure fibred at infinity", that is, a class of Lie structures at infinity that induce in a precise way a fibre bundle structure on a…
The holonomy algebras of Einstein not Ricci-flat pseudo-Riemannian manifolds of arbitrary signature are classified. As illustrating examples, the cases of Lorentzian manifolds, pseudo-Riemannian manifolds of signature $(2,n)$ and the…
We study several classes of Riemannian manifolds which are defined by imposing a certain condition on the Ricci tensor. We consider the following cases: Ricci recurrent, Cotton, quasi Einstein and pseudo Ricci symmetric condition. Such…
An extension of the ambient metric construction of Fefferman-Graham to infinite order in even dimensions is described. The main ingredients are the introduction of "inhomogeneous ambient metrics" with asymptotic expansions involving the…
We study a characterization of 4-dimensional (not necessarily complete) gradient Ricci solitons $(M, g, f)$ which have harmonic Weyl curvature, i.e. $\delta W=0$. Roughly speaking, we prove that the soliton metric $g$ is locally isometric…
We study curvature properties of four-dimensional Lorentzian manifold with two-symmetry property. We then consider Einstein-like metrics, Ricci solitons and homogeneity over these spaces.
We investigate the Kahler-Ricci flow on holomorphic fiber spaces whose generic fiber is a Calabi-Yau manifold. We establish uniform metric convergence to a metric on the base, away from the singular fibers, and show that the rescaled…
We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long-standing question of whether or not every…
We investigate the existence of a holomorphic and isometric immersion in the complex projective space for the complete Ricci-flat Kaehler metrics constructed by M. B. Stenzel on the cotangent bundle of a compact, rank one, globally…
We give the global picture of the normalized Ricci flow on generalized flag manifolds with two or three isotropy summands. The normalized Ricci flow for these spaces descents to a parameter depending system of two or three ordinary…
We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.